Math 204B - Number Theory

Course description: This is the second in a sequence of three courses, which together constitute an introduction to algebraic and analytic number theory. Part A treated the basics of number fields (their rings of integers, failure of unique factorization, class numbers, the Dirichlet unit theorem, splitting of primes, cyclotomic fields, and more). In part B, we will focus on local fields and local properties of number fields (completions of number fields, finite extensions of local fields, ramification, different and discriminant, decomposition and inertia groups), adeles and ideles, and the basics of local and global class field theory. Part C will focus on zeta functions and L-functions.

Instructor: Kiran Kedlaya, kedlaya [at] ucsd [etcetera]. Office hours: Th 11-12, in APM 7202.

Lectures: MWF 10-10:50, in APM 7421.

Textbook: No required text. Recommended: Algebraic Number Theory (Springer) by J. Neukirch. If you do not already have a copy, I suggest downloading the PDF version from any UCSD computer. Some additional references you might find helpful (but don't try to read them all!):

Prerequisites: Math 204A or equivalent (with instructor's permission).

Homework: Weekly problem sets (4-6 exercises), due on Wednesdays.

Final exam: None.

Grading: 100% homework.



Topics covered so far: